login
Decimal expansion of limit of a power tower: t(2)^(t(3)^(t(5)^(t(7)^(...)))) where t(n)=n^(1/n!) and n takes on consecutive prime values.
1

%I #9 Apr 27 2021 12:46:22

%S 1,5,1,7,7,7,2,3,6,6,2,1,5,2,7,5,3,9,9,7,4,3,3,6,7,3,3,5,1,8,6,9,6,2,

%T 3,2,6,5,6,0,7,8,9,9,8,3,9,4,6,3,4,9,7,4,6,9,3,6,5,5,4,0,4,3,8,0,0,5,

%U 4,4,0,9,0,3,8,9,0,7,6,8,4,5,4,4,8,9,4,7,0,4,4,0,4,7,4,6,5,8,6,9

%N Decimal expansion of limit of a power tower: t(2)^(t(3)^(t(5)^(t(7)^(...)))) where t(n)=n^(1/n!) and n takes on consecutive prime values.

%e 1.51777236621527539974336733518696232656078998394634974693655404380054409...

%o (PARI) default(realprecision,100); t=0; forstep(n=100,1,-1,t=(prime(n)^(1/prime(n)!))^t); return(t)

%Y Other power towers: A098454, A098584, A100120, A100121.

%K cons,nonn

%O 1,2

%A Mark Hudson (mrmarkhudson(AT)hotmail.com), Nov 11 2004